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The phase diagram of random threshold networks

Szejka, Agnes ; Mihaljev, Tamara ; Drossel, Barbara (2024)
The phase diagram of random threshold networks.
In: New Journal of Physics, 2008, 10 (6)
doi: 10.26083/tuprints-00020547
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: The phase diagram of random threshold networks
Language: English
Date: 5 March 2024
Place of Publication: Darmstadt
Year of primary publication: 6 June 2008
Place of primary publication: London
Publisher: IOP Publishing
Journal or Publication Title: New Journal of Physics
Volume of the journal: 10
Issue Number: 6
Collation: 13 Seiten
DOI: 10.26083/tuprints-00020547
Corresponding Links:
Origin: Secondary publication DeepGreen

Threshold networks are used as models for neural or gene regulatory networks. They show rich dynamical behaviour with a transition between a frozen phase and a chaotic phase. We investigate the phase diagram of randomly connected threshold networks with real-valued thresholds h and a fixed number of inputs per node. The nodes are updated according to the same rules as in a model of the cell-cycle network of Saccharomyces cereviseae (Li et al 2004 Proc. Natl Acad. Sci. USA 101 4781–6). Using the annealed approximation, we derive expressions for the time evolution of the proportion of nodes in the ‘on’ and ‘off’ states, and for the sensitivity λ. The results are compared with simulations of quenched networks. We find that for integer values of h the simulations show marked deviations from the annealed approximation even for large networks. This can be attributed to the particular choice of the updating rule.

Identification Number: Artikel-ID: 063009
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-205472
Classification DDC: 500 Science and mathematics > 530 Physics
Divisions: 05 Department of Physics > Institute for Condensed Matter Physics
Date Deposited: 05 Mar 2024 10:21
Last Modified: 24 May 2024 14:12
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/20547
PPN: 516008072
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